Methods for reducing error rates in data transmission may involve using encoding algorithms to encode data with error correcting codes. At a receiving end, the encoded data is decoded by decoding algorithms to reproduce the originally transmitted data with low occurrences of error. However, highly effective error correcting codes usually require complex decoding algorithms and such complex decoding algorithms can be difficult to implement.
Turbo codes provide a compromise between error correction and decoder complexity. Turbo codes employ concatenated coding in which two or more constituent codes are used sequentially or in parallel, usually with some form of an interleaver structure in between. The first constituent code has codewords used for checking and correcting of the data being encoded. The second constituent code has codewords used for checking and correcting of the data being encoded after interleaving. Individually the constituent codes are of limited effectiveness in error correction, but depending on the interleaver structure, the combination of the two constituent codes is surprisingly effective, if a proper decoding algorithm is used.
The interleaver permutes the data being encoded to ensure that data being encoded for which one constituent code has low-weight codewords causes the other constituent code to have high-weight codewords. The weight of a codeword is defined as the number of nonzero coordinates in the codeword. How well interleaving succeeds in ensuring high-weight codewords depends on the depth of interleaving and the interleaver structure. Interleaver depth is defined to be the maximum difference in position that a symbol in the data being encoded has before and after interleaving. The greater the interleaver depth, the greater likelihood that the codewords of the two constituent codes favorably complement each other to create highly effective error correction for the data being encoded.
At the receiving end, the two constituent codes are decoded with respective decoders to produce estimates of the data before encoding. Each decoder decodes its respective constituent code and sends a posteriori data estimates, estimates based only on received encoded data, to the other decoder. Each decoder then uses the a posteriori estimates from the other decoder as a priori information to produce a priori estimates, estimates based on prior information known about the encoded data. A priori estimates from each decoder are sent to the other decoder to produce new a priori estimates. This last step is iterated several times to yield progressively better a priori estimates until satisfactory convergence is reached. The generation of an a priori or a posteriori estimate is referred to as a decoding iteration.
In spite of their powerful error correcting capability, turbo codes are generally viewed as more suitable for applications that do not have stringent delay requirements. However, it may be desirable to reduce delays associated with decoding in turbo codes to take advantage of their relatively simple implementation and error correction strengths in certain applications.